(USA TODAY) While urging House Republicans to back new immigration legislation, President Obama said Monday he is willing to split a bill into pieces if that will get it passed.

"That's okay," Obama said during a speech in San Francisco. "It's Thanksgiving. We can carve that bird into multiple pieces - a drumstick here, breast meat there."

But Obama also said a final package must include certain elements, including a proposed pathway to citizenship that has drawn opposition from Republicans.

Said Obama: "As long as all the pieces get done, soon, and we actually deliver on the core values we have been talking about for so long, I think everybody is fine with it."

Obama caught flak during his speech as protesters yelled at him over the number of deportations during his time in office.

"Stop deportations! Stop deportations!" protesters chanted.

The president said he is bound by the law. When someone yelled he had the "power" to stop deportations, Obama replied, "Actually, I don't. And that's why we're here."

Obama told the protesters that it's "easy" to shout about problems, but he is seeking a harder path designed "to use our democratic processes to achieve the same goal that you want to achieve. But it won't be as easy as just shouting."

The Democratic-led Senate passed an immigration bill earlier this year; the Republican-run House has not taken action on the issue.

House Speaker John Boehner, R-Ohio, has said Republicans want to take a "step-by-step" approach to immigration challenges.

"The American people are skeptical of big, comprehensive bills, and frankly, they should be," Boehner said last week. "The only way to make sure immigration reform works this time is to address these complicated issues one step at a time."

Obama, who has offered the piecemeal approach before, said a final immigration package should include strengthened border security, punishment for businesses that knowingly hire undocumented workers, and a modernization of the immigration system.

He also advocated "a pathway to earned citizenship" for people who are already in the country illegally, a sticking point in past immigration debates in Congress.

Many Republicans oppose a pathway to citizenship, likening it to amnesty to lawbreakers.

Sen. Jeff Sessions, R-Ala., who opposed the immigration bill in the Senate, said the issue surfaces at a time of high unemployment and flat wages.

"The president must be asked - by media and lawmakers alike -- how he can possibly justify a plan that will double the flow of immigrant workers at a time when 91.5 million Americans are outside the labor force?" Sessions said.

During his speech, Obama said immigration is not just a problem along the U.S.-Mexican border, saying, "We're blessed with immigrants from all over the world."

Obama spoke at the Betty Ann Ong Chinese Recreation Center in San Francisco, part of a three-day trip focused mainly on campaign fundraising. (Ong was a flight attendant who died on 9/11.)

Many people study in the United States, then take their skills back to their home countries, Obama said, adding, "We're training our own competition."

He pointed out that many Republicans, including predecessor George W. Bush, support immigration changes. The president didn't mention it, but many Republicans cite a decline in Hispanic support for the GOP as a major election problem.